A unified theory of finite-state recognisability

Información del proyecto

LIPA

Identificador del acuerdo de subvención: 683080

DOI

10.3030/683080

Proyecto cerrado

Fecha de la firma de la CE 26 Abril 2016

Fecha de inicio 1 Mayo 2016

Fecha de finalización 31 Octubre 2021

Financiado con arreglo a

• EXCELLENT SCIENCE - European Research Council (ERC)

Coste total

€ 1 768 125,00

Aportación de la UE

€ 1 768 125,00

Coordinado por

UNIWERSYTET WARSZAWSKI
Poland

Periodic Reporting for period 4 - LIPA (A unified theory of finite-state recognisability)

Período documentado: 2020-11-01 hasta 2021-10-31

Resumen del contexto y de los objetivos generales del proyecto

The main goal of the project is to produce a unified theory of finite state devices which recognise properties of words, trees, graphs, etc. The literature contains a wide array of results on this topic, but a unifying framework is lacking. The project proposes such a framework, using monads and Eilenberg-Moore algebras, which are concepts known from category theory. The main goal of the project is to use monads and their algebras to understand finite state devices in contexts where they are not properly understood, and to place this understanding inside a uniform framework. Two specific areas of focus for the project are: (a) finite state devices which process graphs and trees; and (b) transductions, i.e. devices which produce outputs, like words or trees, as opposed to just yes/no answers.

Trabajo realizado desde el comienzo del proyecto hasta el final del período abarcado por el informe y los principales resultados hasta la fecha

The main achievements of the projects are:
1. A thorough development of the theory of recognisable languages over monads, which is summarised in a draft book called "Languages recognised by (...)". This book can be found on the PI's web page.
2. The resolution of Courcelle’s conjecture about MSO on graphs of bounded treewidth. This result puts the finishing touches on a project started by Courcelle, i.e. understanding to what degree algebra and logic coincide on graphs.
3. A non-elementary lower bound on the complexity of the reachability problem in Petri nets [21] . This is the first progress since over 40 years on a fundamental model of computation, and was awarded the best paper award at STOC 2019.
4. The introduction of the class of polyrergular functions [15, 38]. This class can be seen as an answer to the question: "what is polynomial time finite state computation?"
5. The introduction of vector spaces of orbit-finite dimension [37]. This notion combines two relaxations of finiteness: (a) having finite dimension; and (b) being orbit-finite. The combination turns out to be surprisingly fruitful.

Avances que van más allá del estado de la técnica e impacto potencial esperado (incluida la repercusión socioeconómica y las implicaciones sociales más amplias del proyecto hasta la fecha)

The work discussed above creates a solid unifying framework for existing work (the monads), solves open problems (Courcelle's conjecture and Petri nets), and creates new fields of study (polyregular functions and orbit-finite dimension).

Logo of the project